A gold nugget has a density of 19.3 g/cm3. The mass of the gold nugget is 71.22 g if the nugget has a volume of 0.00369 l.
How does density work?Mass per unit volume of a material substance; density. Density is defined as d = M/V, where M stands for mass, and V for volume. The unit of density that is most frequently used is grams per cubic centimeter.
Density = 19.3g/cm³
Volume = 0.00369l
mass = ?
Formula
Density = mass/ volume
mass = density x volume
Convert volume from liters to cubic centimeters
1 l -------- 1000 cm³
0.00369l --------- x
x = (0.00369 x 1000 )/1
x = 3.69 cm³
Substitution
mass = 19.3 x 3.69
mass = 71.22 g.
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find the amplitude, frequency, and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is the following.
The amplitude is 0.25s.
Calculation:
Amplitude = A = 0.225 m
Angular frequency = w = 8π rad/s.
Frequency = f = w/2π = 8π/2πHZ = 4 HZ
Time period = T = 1/f = (1/4)s = 0.25s.
The maximum displacement or distance traveled by a point on an oscillating body or shaft, measured from the equilibrium position. This corresponds to half the length of the vibration path. Amplitude difference between a rest position and maximum shaft deflection.
Frequency The number of waves passing a particular point per second. Duration How long it takes for a wave cycle to complete. Sound wave amplitude is a measure of wave height. The amplitude of a sound wave can be defined as the magnitude or loudness of the maximum displacement from the average position of the vibrating particles in the medium when the sound was produced.
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How do I calculate the force needed to lift an object of 15N at a constant speed of 2m/s?
The force necessary to lift an object is the same as the force necessary to fight gravity.
We may calculate the gravitational force acting on the object using Newton's second law if we assume that the acceleration caused by gravity is 9.8ms2. By exerting force that is produced by the person's muscles, the weights are raised. It is therefore a muscular force. Lift can be in any direction with respect to gravity, contrary to the popular understanding of the word, which defines it with respect to the direction of flow rather than the direction of gravity. If the force on an object's bottom is greater than the force of gravity coming from above, lift will result. Lift must equal gravity for a height to be sustained.
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a) Calculate the ratios of longitudinal modulus of the composite to the matrix modulus for glass/epoxy and carbon /epoxy composites with 10% and 50% fibers by volume. Elastic modules of glass fibers, carbon fibers and epoxy resin are 70, 350, and 3.5 GPa, respectively.
b) Discuss what is the effect of the fibers in the elastic modulus of the composite in the longitudinal direction (2-3 phrases.)
carbon fibers and epoxy resin have respective tensile strengths of 70, 350, and 3.5 GPa. According to these estimates, fibers are particularly effective at increasing the composite modulus in the longitudinal direction.
(a) [tex]V_{f}[/tex]=[tex]A_{f} /A_{c}[/tex] ,[tex]V_{m} =A_{m}/A_{c}[/tex]
The elastic modulus of the composite is given by
E[tex]_{c}[/tex]=[tex]E_{f} V_{f} +E_{m} V_{m}[/tex]
E[tex]_{c}[/tex]/E[tex]_{m}[/tex]=([tex]E_{f} /E_{m}[/tex] - 1) [tex]V_{f}[/tex]+1
the calculation will give the following result
System([tex]E_{f} /E_{m}[/tex]) [tex]V_{f}[/tex]=10% [tex]V_{f}[/tex]=50%
Glass – epoxy(20) 2.9 10.5
Carbon epoxy (100) 10.9 50.5
(b) 50 It has been found that as the volume fraction of fiber grows by a factor of 5, the ratio (E[tex]_{c}[/tex]/E[tex]_{m}[/tex]) similarly increases by a corresponding amount (3.62 for glass epoxy and 4:63 for carbon epoxy )
Additionally, as the fiber modulus increases by a factor of 5, the ratio of (E[tex]_{c}[/tex]/E[tex]_{m}[/tex]) increases by a comparable factor (3.7 at [tex]V_{f}[/tex]=10% and 4.81 at [tex]V_{f}[/tex] =50%). These calculations demonstrate that fibers are particularly successful in raising the composite modulus in the longitudinal direction.
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X ft See the framing plan above. If the image doesn't display, click this link or this link. Assume that There are two girders and 5 beams Each beam spans between two girders (i.e., from grid line 1 to 3) There are four columns (at A/1, A/3, E/1 and E/3) What is the tributary area for a rim joist? (Although not explicitly shown, assume that there are joists directly above the girders. The dimensions of the building are as follows: X = 96 ft . Y = 36 ft A B © D (E) Girder 1 Joist EQ. (2 Y ft EQ Girder EQ. EQ. EQ EQ. X ft
There are two girders and 5 beams Each beam spans between two girders. The tributary area of rim joist is 864ft²
Length of the rim joist = Y ft = 36ft
Length of each bay out of 4 = X/4 = 96/4 = 24ft
Tributary width of rim joist is half on each bay to its side
Tw = 24/2 + 24/2 = 24
Tributary area Ta = tw × length
Ta = 24 × 36 = 864ft²
The floor or roof area (in plan) that results in loading on a certain structural element is known as the tributary area. In each direction, name the adjacent column.
the distance between the two, measured.
multiplying by two the distance
From here, create a perpendicular line.
Repeat until a bounding polygon appears for each gridline that is close by.
A beam's tributary area is equal to its length times the addition of half its space to each adjacent girder.
The square footage of the deck surface area supported by one post is known as the tributary area. Depending on how the deck is set up, this can differ for each post.
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What type of timer would you use to measure
the period of a simple pendulum? How many
oscillations would you time?
It is easy to measure the period using the photogate timer.
What is photogate timer?Photogate timer is used to study free fall, rolling objects, collisions, and pendulums. Photogates allow for extremely accurate timing of events within physics experiments, for studying free fall, air track collisions, pendulum periods, the speed of a rolling object, among other things.
To measure the period of a simple pendulum, we set the simple pendulum into oscillation. Let's say 10 oscillations. The time to complete this oscillation is recorded. This time is divided by the no of oscillation to get the period. Period is also measured in second.
This means that period of a simple pendulum is given as T = t/n
where T is the period and t is the time to complete a given oscillation.
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Light of 650 nm wavelength illuminates a single slit of width 0.20 mm. (Figure 1) shows the intensity pattern seen on a screen behind the slit. You may want to review (Pages 941 - 943) . Figure1 of 1The graph shows intensity as a function of distance. Distance is measured from 0 to 3 centimeters on the x-axis. No values or units are given for the intensity on the y-axis. A large central peak is positioned at 1.5 centimeters with much smaller secondary and tertiary peaks flanking it. The width of the central peak is 1 centimeter. The secondary peaks are positioned at approximately 0.67 centimeters and 2.3 centimeters. The graph shows intensity as a function of distance. Distance is measured from 0 to 3 centimeters on the x-axis. No values or units are given for the intensity on the y-axis. A large central peak is positioned at 1.5 centimeters with much smaller secondary and tertiary peaks flanking it. The width of the central peak is 1 centimeter. The secondary peaks are positioned at approximately 0.67 centimeters and 2.3 centimeters.
Part A What is the distance to the screen? Express your answer to two significant figures and include the appropriate units.
The intensity pattern visible on a screen behind the slits can be stated to depend on the screen's distance (d=1.168m).
How to solve ?From the question we are told,
Two slits that are 0.20 mm apart are illuminated by 650 nm light. The intensity pattern shown on a screen behind the slits is depicted in (Figure 1).
Typically, the mathematical formula for the distance is as follows:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
d=0.33x10^-2x0.23x10^-3/650x10^-9
d=1.168m
What purpose does the distance formula serve?The distance formula is a formula used to determine how far apart two places are from one another. The dimensions of these points are unlimited. For instance, you could need to determine the separation between two points in space, a plane, or a line (1, 2, or 3 dimensions) (3d).
How far is that?Distance is the overall, directionless movement of an object. Distance can be characterized as the amount of space an object has covered, regardless of the starting or ending location.
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If two metal blocks of different masses slide freely down the same frictionless incline,
which one of the following is true?
A) They have equal accelerations
B) They have unequal accelerations, but the forces acting on them are equal.
C) The more massive block reaches the bottom first.
D) The less massive block reaches the bottom first.
E) None of these is correct.
If two metal blocks of different masses slide freely down the same frictionless incline, option a is correct.
Objects accelerate due to imbalanced forces. However, not every item accelerates at the same rate in the presence of the same imbalanced force. As a result, the speed and net force in the direction perpendicular to the plane must both be zero. Since the plane is assumed to be "frictionless," no force is applied to the block that is perpendicular to the surface by the plane. The acceleration is determined by multiplying the acceleration of gravity by the sine of the angle for a frictionless incline of angle degrees. The force of gravity is not parallel to the surface when there is an inclination. The normal force diminishes as the angle of the incline increases, which reduces the frictional force. You can increase the inclination until the thing barely starts to slip.
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find the degeneracy of the second, third, fourth, and fifth levels for the threedimensional cubical box.
The degeneracies of the first, fourth and fifth energy levels for the three dimensionsal cubical box are 1, 3 and 1.
Calculation :
Given Data
A three-dimensional cubic box with
lx=ly=lz=Li.
For a 3D cubic box, the energy of the particle in a box is having a formula given below,
E3D=h²8m(n²x/l²x+n²y/l²y+n²z/l²z)
Given,
lx=ly=lz=Li, put in the above equation, we get,
E3D=h²/8m(n²x/L²+n²y/L²+n²z/L²)
E3D=h²/8mL²(n²x+n²y+n²z)
Now, for the First energy level, the energy will be,
E3D=h²/8mL²(1²+1²+1²)
E3D=3h²/8mL²
The degeneracy is equal to 1 because nx=ny=nz=1.
Now, for the Fourth energy level, the energy will be,
E3D=h²/8mL²(1²+1²+3²)
E3D=h²/8mL²(1+1+9)
E3D=11h²8mL²
The degeneracy is equal to 3 because, nx=1,ny=1,nz=3,nx=1,ny=3,nz=1 and nx=3,ny=1,nz=1.
Now, for the Fifth energy level, the energy will be,
E3D=h²/8mL²(2²+2²+2²)
E3D=h²/8mL²(4+4+4)
E3D=12h²/8mL²
The degeneracy is equal to 1 because nx=2,ny=2,nz=2.
Therefore, the degeneracies of the first, fourth and fifth energy levels are 1, 3 and 1.
Energy levels are degenerate if they correspond to two or more different measurable states of a quantum system. Conversely, two or more distinct states of a quantum mechanical system are said to be degenerate if they have the same energy value when measured. The number of different states corresponding to a particular energy level is called the degeneracy of the level.
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a 1.8-cmcm-tall object is 22 cmcm to the left of a lens with a focal length of 11 cmcm . a second lens with a focal length of -5 cmcm is 37 cmcm to the right of the first lens.
A lens with an 11 cm focal length is 22 cm to the left of a 1.8 cm tall object. The image's height has decreased by 0.25 pixels when a second lens with a focal length of -5cm is placed 37cm to the right of the first lens.
Let's determine the distance at which the image is formed from the first lens since the image of the first lens serves as a virtual object for the second lens. Use the lens manufacturer's formula:
1/o + 1/i = 1/f, where I am the image distance and o is the object distance,
1/i = 1/f - 1/o = 1/(11cm) - 1/(22cm) = 0.045 1/cm, so
i = 22cm
the virtual object for the second lens is left at a distance of 37 cm - 22 cm, or 15 cm, from the second lens. Utilize the lens manufacturer's formula once more:
1/i = 1/f - 1/o (This time, the object distance is the separation between the second lens and the virtual object.)
1/i = 1/(-5cm) - 1/(15cm) = -0.26 1/cm, so
i = -15/4cm away from the second lens.
The sum of the two magnifications from the two lenses is the total magnification: m = m1m2, where m = -i/o, so
m = (-22 cm/22 cm)( 15/4cm/15cm) = -0.25, Consequently, the image's height is 0.25 pixels shorter than it was before.
It is the inverse of the system's optical power that determines how strongly an optical system diverges or converges light: the focal length. The convergence or divergence of light is indicated by a positive focal length, whilst the opposite is true for a negative focal length.
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A gymnast uses a flexible stick to jump over the bar. Which of the following
describes energy changes when he reaches the highest point of his jump?
When the gymnast starts to jump his potential energy starts to convert to kinetic energy. But when he reaches the maximum height and stop there for seconds, potential energy regains. Thus, option C is correct.
What is potential energy?Potential energy of an object is the energy stored in it by virtue of its position. Potential energy increases with increases in mass and height which is clear from the equation for potential energy
p = mgh
Kinetic energy is generated by motion of the object. Thus, only a moving body attains a kinetic energy. Kinetic energy depends on the mass and velocity of the object.
Here, the gymnast gains a kinetic energy when he starts to jump from rest. But, when he reaches the maximum height where the speed slows down, his kinetic energy converts to potential energy. Thus, option C is correct.
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Your question is incomplete. But your complete question probably was:
A gymnast uses a flexible stick to jump over the bar. Which of the following
describes energy changes when he reaches the highest point of his jump?
A) kinetic- potential- potential
B) kinetic- potential- kinetic
C) potential - kinetic – potential
D) potential- potential- kinetic
A penguin slides on ice.
A. Newton's First Law of Motion
B. Newton's Second Law of Motion
C. Newton's Third Law of Motion
Answer:
Newton's first law: An object at rest remains at rest, or if in motion, remains in motion at a constant velocity unless acted on by a net external force.
A potato falling vertically downward is struck by a dart that is traveling vertically upward, as shown above. The dart and potato then collide, stick together, and continue moving after the collision.The weight of the dart is W. Which of the following claims best describes the magnitude of the net force on the dart immediately before, during, and immediately after the collision with the potato?
Option B is Correct
The velocity of the center of mass remains constant before the collision, when they collide there is a slight decrease in kinetic energy of the system since the collision is inelastic, resulting in a slight decrease of velocity, afterwards the velocity is constant again.
Velocity is the directional velocity of a moving object, observed from a given frame of reference and indicating the rate of change of position measured at a given time reference (eg 60 km/h northward). Velocity is a fundamental concept in kinematics, a branch of classical mechanics that describes the motion of bodies.
Velocity is a physical vector quantity. Both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is called velocity, and its magnitude is a consistent derived unit measured in the SI (metric) system as meters per second (m/s or m⋅s−1). For example, " meters/second" is a scalar, but "5 meters/second east" is a vector. An object is said to be accelerating if its velocity, direction, or both change.
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A triathlon athlete swims at an average rate 2.4 miles per hour, and bikes at an average rate of 16.1 miles per hour. At the end of one training session, she has swum and biked more than 20 miles in total.
The inequality and this graph represent the relationship between the hours of swimming, , the hours of biking, , and the total distance the athlete could have traveled in miles. Graph of an inequality. Hours of biking. Hours of swimming.
Mai said, "I'm not sure the graph is right. For example, the point is in the shaded region, but it's not realistic for an athlete to swim for 10 hours and bike for 3 hours in a training session! I think triathlon athletes generally train for no more than 2 hours a day."
Write an inequality to represent Mai's last statement. Graph the solution set to your inequality. Determine a possible combination of swimming and biking times that meet both the distance and the time constraints in this situation.
Elena is considering buying bracelets and necklaces as gifts for her friends. Bracelets cost $3, and necklaces cost $5. She can spend no more than $30 on the gifts. Elena needs at least 7 gift items.
This graph represents the inequality , which describes the cost constraint in this situation.
Let represent the number of bracelets and the number of necklaces.
Graph of inequality. Number of necklaces. Number of bracelets.
Write an inequality that represents the number of gift items that Elena needs.
On the same coordinate plane, graph the solution set to the inequality you wrote.
Use the graphs to find at least two possible combinations of bracelets and necklaces Elena could buy.
Explain how the graphs show that the combination of 2 bracelets and 5 necklaces meet one constraint in the situation but not the other constraint.
Combination of swimming and biking times that meets distance and the time constraints in this situation is s + b ≤ 2. An inequality that represents number of gift items that Elena needs is : 3b+5n≤30.
How is the inequality equation written?If athletes train for not more than 2 hours a day, then the sum of the hours training swimming 'a' and biking 'b' should be less than or equal to 2. Hence, we can write the following inequality:
s + b ≤ 2
Inequality that represents Mai's statement is:
s + b ≤ 2
Part 2:
It is given that , bracelets cost $3, necklaces cost $5 and she can spend not more than $30
Then the inequality that represents the number of gift items that Elena needs : 3b+5n≤30
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A roller coaster starts from rest at point A. If you ignore friction and take the zero of potential energy to be at C, A) the kinetic energy of the coaster at D will be equal to its potential energy at A. B) the kinetic energy of the coaster at E will be equal to its potential energy at C. C) the kinetic energy of the coaster at C will be equal to its potential energy at A. D) the kinetic energy of the coaster at B will be equal to its potential energy at C E) None of these is correct. 13. Two objects are sliding at the same speed across a wooden surface. The coefficient of kinetic friction between the first object and the surface is twice that between the second object and the surface. The distance traveled by the first object before it stops is S. The distance traveled by the second object is A) impossible to determine without knowing the masses involved. B) 28 C) S/2 D) S E) 4S 14. A person of weight w is in an upward-moving elevator when the cable suddenly breaks. What is the person's weight measured in the elevator immediately after the elevator starts to fall? A) w B) greater than w C) less than w D) 9.81w E) zero A force F produces an acceleration a on an object of mass m. A force 3F is exerted on a second object, and an acceleration 8a results. What is the mass of the second object? A) 3m B) 9m C) 24m D) (3/8)m E) (8/3)m 15.
A roller coaster starts from rest at point is option C) the kinetic energy of the coaster at C will be equal to its potential energy at A.
Since Two objects are sliding at the same speed across a wooden surface. The distance traveled by the second object is option B) 2S
A person's weight measured in the elevator immediately after the elevator starts to fall is option E) zero A force F produces an acceleration a on an object of mass m.
The mass of the second object is option D) (3/8)m.
What happens when kinetic energy is equal to potential energy?The amount of kinetic energy change and the amount of potential energy change are identical in all physical processes that take place in closed systems. When the kinetic energy rises, the potential energy falls, and vice versa.
Wave speed is the number of meters a wave travels in a second, or the distance a wave travels in a particular amount of time. Equation Speed = Wavelength x Frequency describes how wave speed relates to wave wavelength and wave frequency.
Therefore, When wavelength and frequency are known potential energy stored energy that depends on the relative positions of different components of a system may be utilized to compute wave speed—this equation can be used to determine wave speed. When stretched or squeezed, a spring has higher potential energy.
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A diffraction grating is illuminated simultaneously with red light of wavelength 690 nm and light of an unknown wavelength. The fifth-order maximum of the unknown wavelength exactly overlaps the fourth-order maximum of the red light. What is the unknown wavelength?
According to the given statement 414 nm is the value of the unknown wavelength.
What is wavelengths and frequency?The distance between two wave crests, which also applies to troughs, is known as the wavelength. Cycles per second (Hz), the number of vibrations that pass across a certain region in a second, is used to measure frequency (Hertz). The link between wavelength and frequency is discussed in this article.
Briefing:For third order maxima,
asinθ = mλ
asinθ = 3 * 690
The slit width in this instance is a, and the angular spacing is.
The fifth order maximum, meanwhile
asinθ = mλ
asinθ = 5λ
Solving as,
5λ = 3 * 690
λ = 414 nm
Therefore, 414 nm is the value of the unknown wavelength.
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A disk of mass M is spinning freely at 4.91 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating.
(a) What is the angular speed of the new system (in rad/s)? rad/s
(b) If a third such disk is dropped on the first two, find the final angular speed of the system (in rad/s). rad/s
(a) The angular speed of the new system is 2.455 rad/s.
(b) The angular speed of the new system is 1.64 rad/s.
(a) The Angular Momentum Conservation Principle is observed since there are no outside forces acting on either disk.The fact that the axes of rotation of each disk coincide allows for the principle to be reduced to its scalar version. The ratio of the inertial moment to the angular speed determines the angular momentum's size. The moment of inertia doubles and the angular speed is cut in half as soon as both disks start to revolve.
It is given by, I ω₀ = 2* I * ωf
Where,
I - Moment of inertia of a disk, measured in kilogram-square meter
ω₀ - Initial angular speed, measured in radians per second
ωf - Final angular speed, measured in radians per second
The expression for relating final angular speed to initial angular speed is,
ωf = 1/2 * ω₀
Given that, ω₀ = 4.91 rad/s
The new system's angular speed is,
ωf = 1/2 * 4.91 = 2.455 rad/s
(b) If third such disk is dropped on the first two, the expression on angular velocity becomes,
I ω₀ = 3* I * ωf
ωf = 1/3* ω₀ = 1/3* 4.91 = 1.64 rad/s.
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A uniform rod of length L, mass M, is suspended by two thin strings. Which of the following statements is true regarding the tensions in the strings?
the following statements is true regarding the tensions in the strings is T2 = 0.6 T1 .
How can you tell how taut a string is?A specific strand, string, or rope is put under stress by the forces pulling on it from each end.Consider the formula for force: mass times acceleration.
What alters a string's tension?Every gauge of a string, the duration of the vibrating string, as well as the frequency of a vibrations along the duration of the string all work together to determine the overall stress on the string. Depending on what kind of metal was used to connect the strings, they may have a varying tension.
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a 1.0kg block and a 2.0 kg block are pressed together and both are on a horizontal fricitionless surface with a compressed light spring between them concerning the states of the two blocks after they are released and detached from the spring which of the following statements is correct
The spring and pan have very little mass. The mass executes a SHM when it is lightly squeezed and then released.
Forces, location, velocity, and energy—both kinetic and potential energy—are some examples of these quantities. Hoare's Rule. Energy conservation: When the compressed spring returns to its natural length, all of the energy that was stored in it is transformed into kinetic energy. The block is propelled along a horizontal surface as the spring is let go. Friction and the spring's bulk can be disregarded. Between two blocks with masses of 1 kg and 2 kg that are lying on a smooth horizontal surface is a compressed elastic spring. The block is freed from rest once the spring has been compressed by 2.0 cm.
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An oscillator creates periodic waves on two strings made ofthe same material. The tension is the same in both strings.If the strings have different thicknesses,which of the following parameters, if any, will be different in thetwo strings?Check all that apply.wave frequencywave speedwavelengthnone of the aboveIf the strings have the same thickness butdifferent lengths, which of the following parameters, if any, willbe different in the two strings?Check all that apply.wave frequencywave speedwavelengthnone of the above
Wavelength of the following parameters, if any, will be different in the two strings.
What is wavelengths and frequency?The distance between two wave crests, which also applies to troughs, is known as the wavelength. Cycles per second (Hz), a unit of measurement for frequency, is the number of vibrations that pass through a certain space in a second (Hertz). The link between frequency and wavelength is discussed in this article.
Briefing:The formula for the wave's speed on the string is
[tex]$v=\sqrt{\frac{T}{\mu}}$[/tex]
Here, mu stands for mass per unit of length and T for string tension.
The mass per unit length varies depending on the thickness. As a result, the wave speed varies between the two strings.
The oscillator determines the frequency of the oscillations. As a result, using the same oscillator, the frequency is the same for the two strings.
In terms of frequency and speed,
f= γλ
λ= f/γ
The wavelength of the waves varies as the speeds vary since the frequency is constant.
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what is the amplitude and period of this wave? I WILL MARK BRAINLIEST!
Answer:
amplitude:1m
period:10s
Explanation:
the free-fall acceleration at the surface of planet 1 is 12 m/s2m/s2. the radius and the mass of planet 2 are twice those of planet 1. What is the free-fall acceleration on planet 2? Express your answer using two significant figures. m/s^2.
The free-fall acceleration on the planet 2 will be 6 m/sec².
Acceleration is the rate of change of velocity with respect to time.
Also it defines the maximum capacity of a vehicle to attain its speed.Its SI unit is m/sec².As we know that acceleration due to gravity can be expressed as
g = MG / R²
M = mass of the planet
G = Gravitational constant
R = radius of the planet
For planet 1
Mass = M1 = M
Radius = R1 = R
Acceleration due to gravity = g1 = 12 m/sec²
G = g1R1²/M1
For planet 2
Mass = M2 = 2M
Radius = R2 = 2R
Acceleration due to gravity = g2 = ?
G = g2R2²/M2
Since 'G' is constant, therefore on equating both the equations, g2 can be calculated
g2 = (g1R1²/M1) * (M2/R2²)
g2 = (12R²/M) * (2M/4R²)
g2 = 6 m/sec²
The free-fall acceleration on planet 2 will be 6 m/sec².
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The bullet strikes a block of wood which exerts, on average, a force of 50,000 N opposing the motion of the bullet. How far does the bullet penetrate?
The distance that the bullet penetrates is 0.03m.
How to solve?Given data:
The mass of the bullet is
m = 25 g = 0.025 kg
The bullet's initial velocity is
u = 350 m/s
The final velocity of the bullet is
v = 0
The average force opposing the motion is
F = 50000N
From Newton's second law, the acceleration derived as,
F = m. a.
a = F. m..........(1)
Substituting values in equation (1), we get:
a = 50000 N / 0.025 kg = 2×106 m/s 2
The equation of motion is,
v 2=u 2−2 a S
2 a S=u 2−v 2
S = u 2−v 2/2 a.......(2)
Substituting values in equation (2), we get:
S = (350 m/s)2−0/2(2×106 m/s 2)
=12.25×104 m/s 4×106 m/s 2=0.03m
here, the distance that bullet penetrates is 0.03m.
What is the kinetic energy equation?Kinetic energy has the following formula: K.E. = 1/2 m v 2, where m is the object's mass and v is its square velocity. The kinetic energy is measured in kg/m per second squared if the mass is measured in kg and the velocity is measured in meters per second.
Which 4 forms of kinetic energy are there?Radiant, thermal, electrical, and mechanical kinetic energies are the basic categories.
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which of the following vectors best describes the path of the airplane? question 6 options: none of these
The following vectors best describes the path of the airplane Aniseed of the as plan is 528 [tex]\mathrm{mi} / \mathrm{hr}[/tex]
What is airplane?
A fixed-wing aircraft that is pushed forward by the thrust of a jet engine, propeller, or rocket engine is known as an aeroplane or aeroplane. There are many different sizes, forms, and wing arrangements for airplanes.
[tex]\text { bearing } 25^{\circ} \text { west of north }[/tex]
[tex]\text { Since } \quad 90^{\circ}+25^{\circ}=115^{\circ}[/tex]
[tex]\text { so path of the airplane is }[/tex]
[tex]\left.v=528 \cos \left(i 15^{\circ}\right) i+528 \sin \left(115^{\circ}\right)\right][/tex]
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A 20 kg crate is placed on a horizontal conveyor belt. The materials are such that μs = 0.41 and μk = 0.21. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up to the right What is the maximum acceleration the belt can have without the crate slipping? If acceleration of the belt exceeds the value determined in part C, what is the acceleration of the crate?
The maximum acceleration for the belt that the slipping of the crate does not appear is 2 m/s².
what is a belt?
Each rotating pulley is supported on a shaft by a belt drive, which transfers motion from one to the next.Pulley belts are often manufactured from a soft, flexible material such as rubber, although shafts and pulley wheels can be made of any material. The pulleys and belts' grooves aid in their ability to grasp and turn.The frictional force between the two surfaces increases with the amount of wrap around the curved surface, and only a portion of that force (or the resulting belt tension) is transmitted to the other end of the belt or rope when a force applies tension to one end of a belt or rope wrapped around a curved surface. The Belt friction equation can be used to model belt friction.To learn more about belt refer to
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a cellist tunes the c-string of her instrument to a fundamental frequency of 65.4 hz. the vibrating portion of the string is 0.615 m long and has a mass of 14.8 g .
(A) With 268.94 N tension must she stretch it.
26% increase in tension is needed to increase the frequency from 65.4 Hz to 73.4 Hz, corresponding to a rise in pitch from C to D.
Part (A)
Fundamental frequency =f0= 65.4 Hz.
The length of the vibrating portion of the string = l = 0.615 m
Mass= m = 14.8 g
We know, [tex]f_0 = \frac{v}{2l}[/tex]
So, the value of v will be 65.4*2*0.615 = 80.442 m/s
As, We know,
[tex]T=\frac{v^2}{\frac{m}{l}}[/tex]
So, the value of tension will be: [tex]\frac{80.442^2}{\frac{14.8}{0.615}}=\frac{6470.91}{24.06}=268.94\:N[/tex]
Part (B)
Fundamental frequency =f0= 73.4 Hz.
The length of the vibrating portion of the string = l = 0.615 m
Mass= m = 14.8 g
We know, [tex]f_0 = \frac{v}{2l}[/tex]
So, the value of v will be 73.4*2*0.615 = 90.282 m/s
As, We know,
[tex]T=\frac{v^2}{\frac{m}{l}}[/tex]
So, the value of tension will be: [tex]\frac{90.282^2}{\frac{14.8}{0.615}}=\frac{8150.8395}{24.06}=338.77\:N[/tex]
So, the percentage increase in tension will be [tex]\frac{338.77-268.94}{268.94}\times 100\%=25.96\% \approx 26\%[/tex]
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The complete question should be:
a cellist tunes the c-string of her instrument to a fundamental frequency of 65.4 hz. the vibrating portion of the string is 0.615 m long and has a mass of 14.8 g .
Part A: With what tension must she stretch it?
Part B
What percent increase in tension is needed to increase the frequency from 65.4 Hz to 73.4 Hz, corresponding to a rise in pitch from C to D?
Does the Foucault pendulum rotate at the poles because they are considered to be the axes of rotation of earth? Why doesn’t the pendulum move at the equator?
Due to the pendulum's sluggish swing, which gave the impression of changing direction as the Earth moved away, the Foucault Pendulum demonstrated that the Earth rotates.
Foucault understood that his pendulum would swing more slowly the longer the thread was linked to the weight.
If he used a very heavy weight and the string above to a nearly frictionless pin, the pendulum would swing so slowly that it would seem to shift direction as the Earth moved away.
Foucault's pendulum revolves at the same speed as the Earth's rotation when they align at the poles. These axes are perpendicular to each other everywhere on the equator, therefore the pendulum is completely unaffected by the Earth's spin.
The first scientific proof of the Earth's rotation on its axis was the rotation of the plane of swing of Foucault's pendulums. There is relative motion between them as the Earth spins beneath a Foucault pendulum that swings back and forth in a plane.
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Using the loop rule and deriving the differential equation for an LC circuit find the current (sign included) through the inductor at the instant t = 2.2 s if L = 3.7 H, C = 5.0 F. The initial charge at the capacitor is Qo = 3.2 C and the initial current through the inductor is lo = 0. = Number i Units
Initial current via the inductor is lo = 0, and initial charge at the capacitor is Q-o = 3.2 C. The only two devices allowed by the loop rule.
Find the current (sign included) flowing through the inductor at the point t = 2.2 seconds using the loop rule and the differential equation derived for an LC circuit. Derive the differential equation for an LC circuit using the loop rule. To improve comprehension of complex concepts in electrical circuit analysis, such as inductance, capacitance, and reactance, By building up electric charges on two nearby surfaces, a capacitor is a device that stores electrical energy in an electric field. An RL circuit is one with resistance and self-inductance, and an RL circuit with a resistor.
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the rod has a diameter of 40 mm. if it is subjected to the force system shown, determine the stress components that act at point a, and show the results on a volume element located at this point
In this case, we are given that the rod is subjected to the force system shown in the figure. There is a vertical force F acting on the rod at point A, as well as a horizontal force P. The rod is also subjected to a moment M about the z-axis.
To determine the stress components that act at point A, we need to consider the forces that are acting on a small volume element located at this point.
The stress on a volume element is defined as the force acting on the element per unit area. The stress components at a point can be represented by a stress tensor, which is a 3x3 matrix with nine elements. The diagonal elements of the stress tensor represent the normal stress components, while the off-diagonal elements represent the shear stress components.
To determine the stress components at point A, we need to consider how these forces are distributed over the surface of the volume element. The normal stress components can be found by considering the forces acting perpendicular to the surface of the element. The shear stress components can be found by considering the forces acting tangent to the surface of the element.
For example, the normal stress component in the x-direction at point A can be found by considering the force F acting perpendicular to the surface of the element in the y-direction. The normal stress component in the y-direction at point A can be found by considering the force P acting perpendicular to the surface of the element in the x-direction. The shear stress component in the XY-plane at point A can be found by considering the moment M acting tangent to the surface of the element.
To determine the specific values of the stress components, we would need to know the dimensions of the volume element, as well as the magnitudes of the forces and moments acting on the rod. With this information, we can use the equations of statics to solve for the stress components at point A.
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Given that A + B = 0, (a) how does the magnitude of B compare with the magnitude of A? (b) How does the direction of B compare with the direction of A?
If A + B = 0, then the magnitude of B is equal to the magnitude of A. This is because the magnitude of a vector is simply its size or length, and if two vectors add up to zero, then their magnitudes must be equal.
As for the direction of B, it is the opposite of the direction of A. This is because if two vectors are equal in magnitude and opposite in direction, their sum will be zero. For example, if A is a vector pointing to the right and B is a vector pointing to the left, their sum will be zero. Similarly, if A is a vector pointing upwards and B is a vector pointing downwards, their sum will also be zero.
In summary, if A + B = 0, then the magnitude of B is equal to the magnitude of A, and the direction of B is opposite to the direction of A.
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Which of the following is an important difference between the infinite square-well potential and the finite square-well potential?a. The number of energy levels is limited in the infinite square-well potential but not limited in the finite square-well potential.b. The infinite square-well potential utilizes Schrödinger's equation to describe particle motion while the finite square-well potential does not.c. The energy levels are quantized only in the finite square-well potential.d. Particles can exist in classically forbidden regions outside the finite square-well potential.e. Only the energy levels in the finite square-well potential depend on Planck's constant.
Particles can exist in classically forbidden regions outside the finite square-well potential.
The correct option is D.
What if Planck's constant was zero?In the absence of quantum effects, everything would be continuous, smooth, and completely predictable in the Newtonian sense. However, we may not be here to get bored with this if Planck's constant were 0.
What use does Planck's constant serve?At the atomic scale, the behavior of both particles and waves is described by Planck's constant. One of the factors that led to the creation of quantum mechanics is Planck's constant. It was a surprise when those boundaries also turned to represent the limits where known rules of physics applied since the Planck scaled was developed as an universal set of units.
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